We introduce the parameter of block elimination distance as a measure how close graph is to some particular class. Formally, given class $${\mathcal {G}}$$ , {B}}({\mathcal {G}})$$ contains all graphs whose blocks belong and {A}}({\mathcal where removal vertex creates in . Given hereditary we recursively define $${{\mathcal {G}}}^{(k)}$$ so that {G}}^{(0)}={\mathcal and, if $$k\ge 1$$ {G}}^{(k)...

Lifted inference algorithms exploit repeated structure in probabilistic models to answer queries efficiently. Previous work such as de Salvo Braz et al.’s first-order variable elimination (FOVE) has focused on the sharing of potentials across interchangeable random variables. In this paper, we also exploit interchangeability within individual potentials by introducing counting formulas, which i...

Multireceiver authentication codes allow one sender to construct an authenticated message for a group of receivers such that each receiver can verify authenticity of the received message. In this paper, we give a formal dee-nition of multireceiver authentication codes, derive information theoretic and combinatorial lower bounds on their performance and give new eecient and exible constructions ...